Teach21 NxG Unit Plan
Unit 6: Connecting Algebra and Geometry through Coordinates
Mathematics High School Math I
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Title: Unit 6: Connecting Algebra and Geometry through Coordinates
Author & Email: Stephanie Smith, slsmith@kcs.kana.k12.wv.us, Crystal Godbey, cgodbey@kcs.kana.k12.wv.us
Grade Level: High School Math I
Unit Overview:
Building on their work with the Pythagorean Theorem in the 8th grade to find distances, students use a rectangular coordinate system to verify geometric relationships, including properties of special triangles, quadrilaterals, and slopes of parallel and perpendicular lines.

Unit Calendar
http://wveis.k12.wv.us/teach21/cso/upload/UP93CAL.doc
Next Generation Content Standards and Objectives:
Objectives Directly Taught or Learned
Through Inquiry/Discovery
Evidence of Student Mastery of Content
M.1HS.CAG.1 
use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1
) lies on the circle centered at the origin and containing the point (0,2).

Lesson 5 – Real World Application Problems

Lesson 5 – Let’s Prove It! Challenge  

Lesson 6 – Going Around in Circles Revisited 

M.1HS.CAG.2 
prove the slope criteria for parallel and perpendicular lines; use them to solve geometric problems (e.g., find the equation of a lines parallel or perpendicular to a given lines that passes through a given point).

(Relate work on parallel lines to work on M.1HS.RWE.3 involving systems of equations having no solution or infinitely many solutions.)

Lesson 1 – Parking Lot Design   

Lesson 2 – Flash Card Activity   

Lesson 3 – Partner Quiz   

Lesson 3 – Parallel and Perpendicular Lines WS   

M.1HS.CAG.3 
use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. (Provides practice with the distance formula and its connection with the Pythagorean theorem.)

Lesson 4 – Distance Formula Proof 

Lesson 4 – Pythagorean Theorem Practice WS
Mathematical Practices::
Mathematical Practices Evidence of Student Engagement in Mathematical Practices
1. Make sense of problems and preserve in solving them. Lessons 3, 4 and 6
2. Reason abstractly and quantitatively. PreReq Lesson 1 and 5
3. Construct viable arguments and critique the reasoning of others. PreReq Lesson 1, Lessons 1, 3 and 5
4. Model with mathematics. PreReq Lesson 1, Lessons 1 and 5
5. Use appropriate tools strategically Lessons 1 and 6
6. Attend to precision. Lessons 2 and 5
7. Look for and make use of structure. Lessons 4 and 5
8. Look for and express regularity in repeated reasoning. Lessons 2 and 4
Focus/Driving Question:
How can we connect Algebra and Geometry through Coordinates?
Student will Know:

Students will know how the distance formula is derived from the Pythagorean Theorem.

Student will Do:
By the end of this unit, students will be able to formulate explanations showing how the distance formula is derived from the Pythagorean Theorem. To do this, students will first prove the slope criteria for parallel and perpendicular lines. Next, students will use that criterion to solve geometric problems. Lastly, students will use coordinates to prove simple geometric theorems algebraically.
Materials/Resources/Websites:

You can find alternative resources, including websites, at the bottom of each lesson plan.

Assessment Plan:

Formative Assessments are found throughout each lesson. Also, there is a summative quiz that assesses the students on their knowledge of the slope criteria for parallel and perpendicular lines. That quiz can be found in Lesson 3.

Major Products:
There are two large projects in this unit. The first project can be found in the Are the Stairs Up to Code lesson. In this lesson, students will work in groups to measure the stairwells in their schools. When complete, each student will individually write a letter to an administrator regarding their school’s building codes and if the school meets these codes. The other major projects can be found in the Parking Lot lesson. In that last portion of the lesson (culminating assessment) students are to construct their own parking lots using their conjectures regarding the slopes of parallel and perpendicular lines.
Unit Reflection:
Because this is the final unit for Math I, it would be nice to take some time to reflect on the entire Math I course, not only this final unit. The students should have compiled a Math I journal that reflects their triumphs, setbacks, and successes throughout this course. Allow the students to review their individual Math I journals and write a reflection piece regarding Math I in its entirety. Which unit did you enjoy the most? What unit was most challenging for you? What topic did we cover that you felt most accomplished after? Allow the students to share these writing pieces with their language arts teacher and your administrators.
Tagged Next Generation Content Standards and Objectives
NxG ID NxG Objectives
M.1HS.CAG.1 use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, v3) lies on the circle centered at the origin and containing the point (0, 2). (CCSS.Math.Content.HSG-GPE.B.4)
M.1HS.CAG.2 prove the slope criteria for parallel and perpendicular lines; use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). (Relate work on parallel lines to work on M.1HS.RWE.3 involving systems of equations having no solution or infinitely many solutions.) (CCSS.Math.Content.HSG-GPE.B.5)
M.1HS.CAG.3 use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. (Provides practice with the distance formula and its connection with the Pythagorean theorem.) (CCSS.Math.Content.HSG-GPE.B.7)
Files Uploaded
File Name Description
UP93WS2.doc 01 Diagonal Parking Lot Worksheet
UP93WS3.doc 01 Another Parking Lot Design Worksheet
UP93WS4.doc 01 Yet Another Parking Lot Design Worksheet
UP93WS5.doc 01 Student Parking Rubric
UP93WS6.doc 01 Porch Problem Rubric
UP93WS7.doc 01 Culminating Assessment Rubric
UP93WS8.doc 01 Diagonal Parking Lot Answer Key
UP93WS9.doc 01 Another Parking Lot Design Answer Key
UP93WS10.doc 01 Yet Another Parking Lot Design Answer Key
UP93WS11.doc 02 Trial Log Worksheet
UP93WS12.doc 02 Flash Cards
UP93WS13.ppt 02 Points and Lines and Slopes, Oh My! PowerPoint
UP93WS14.doc 03 Partner Quiz
UP93WS15.doc 03 Partner Quiz Answer Key
UP93WS16.doc 03 Parallel and Perpendicular Line Practice
UP93WS17.doc 03 Parallel and Perpendicular Line Practice Key
UP93WS18.doc 04 Pythagorean Practice
UP93WS19.doc 04 Pythagorean Practice Key
UP93WS20.doc 04 Proving the Distance Formula Worksheet
UP93WS21.ppt 04 Proving the Distance Formula PowerPoint
UP93WS22.doc 04 Practice Handout
UP93WS23.doc 04 Practice Handout Key
UP93WS24.pdf 05 Let's Prove It Challenge
UP93WS25.pdf 05 Let's Prove It Organizer Key
UP93WS26.pdf 05 Let's Prove It Organizer
UP93WS27.pdf 05 Real World Exit Homework Key
UP93WS28.pdf 05 Real World Exit Homework
UP93WS29.pdf 05 Scavenger Hunt
UP93WS30.doc 06 Going Around in Circles Card Set Equations
UP93WS33.ppt 06 Going Around in Circles PowerPoint
UP93WS34.doc 06 Poster Activity Template
UP93WS35.doc 06 Poster Activity Template Solutions
UP93WS37.doc PreReq 1 Are the Stairs up to Code Worksheet
UP93WS38.pdf PreReq 1 Letter Rubric
UP93WS39.doc PreReq 1 Are the Stairs up to Code Worksheet Key
UP93WS40.pdf 06 Solutions - Going Around in Circles Revisited
UP93WS41.pdf 06 Going Around in Circles Revisited
UP93WS42.pdf 06 Going Around in Circles Common Issues
UP93WS43.pdf 06 Lesson Plan
Date Created: May 31, 2012
Date Modified: August 06, 2012
Unit Plan Outline
(Lesson Plans)

Prerequisite Lesson: Are the Stairs Up to Code? Slope Review


Lesson 1: Parking Lot: Parallel and Perpendicular Lines on a Coordinate Plane


Lesson 2: Points and Lines and Slopes, Oh My!


Lesson 3: Slope and Parallel/Perpendicular Lines Quiz/Practice


Lesson 4: Connecting the Pythagorean Theorem/Distance Formula


Lesson 5: Let’s Prove It!


Lesson 6: Going Round in Circles


Lesson 7: Working with Sydney

Career Connections:
Many of the lessons in this unit center around real life applications and careers that use mathematical concepts. For example, the lesson Are the Stairs Up to Code asks the students to measure their school’s stairwells and compare their slopes with their county building regulations. Also, the Parking Lot lesson asks students to create parking lot models based on their conjectures regarding the slopes of parallel and perpendicular lines.

Key Word Search Fields Coordinates, Pythagorean Theorem

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